ADMM-Based Distributed Kalman-like Observer with Applications to Cooperative Localization

TL;DR

This paper introduces a distributed Kalman-like observer for multi-agent systems that uses ADMM for efficient, local computation and communication, improving scalability and stability in cooperative localization tasks.

Contribution

It proposes a novel ADMM-based distributed observer with sparsity-preserving prediction and stability analysis, avoiding dense Riccati recursion and centralized computations.

Findings

The proposed scheme achieves distributed state estimation with local communication only.

The observer's estimation error dynamics are proven to be uniformly exponentially stable.

Numerical simulations demonstrate effective cooperative localization performance.

Abstract

This paper addresses distributed state estimation for multi-agent systems with local and relative measurements, motivated by cooperative localization problems in which the global state dimension scales with the size of the network. We consider a Kalman-like observer in information form and introduce a sparsity-preserving prediction step based on an exponential forgetting factor, thereby avoiding the dense Riccati recursion of the standard information filter. The correction step is recast as a strongly convex quadratic program with structure induced by the sensing graph, which enables a distributed solution based on the alternating direction method of multipliers (ADMM). In the resulting scheme, each agent updates local copies of its own correction variable and those of its neighbors using only local communication, thus avoiding centralized matrix inversion and consensus over full global-state quantities. A two-time-scale stability analysis is developed for the interconnected observer: the reduced estimation-error dynamics are shown to be uniformly exponentially stable, the ADMM dynamics define an exponentially stable fast subsystem, and these properties are combined to establish uniform exponential stability of the overall distributed observer. Numerical simulations in a multi-agent cooperative localization scenario illustrate the performance of the proposed distributed observer.